In (Chen and Kulik, 2009), a method of renormalization was proposed for constructing some more physically
realistic random potentials in a Poisson cloud. This paper is devoted to the
detailed analysis of the asymptotic behavior of the annealed negative exponential moments
for the Brownian motion in a renormalized Poisson potential. The main results
of the paper are applied to studying the Lifshitz tails asymptotics of the integrated density
of states for random Schrödinger operators with their potential terms represented
by renormalized Poisson potentials.

Xia Chen

Alexey Kulik

Asymptotics of Negative Exponential Moments for Annealed Brownian Motion in a Renormalized Poisson Potential

We consider the Cauchy-Dirichlet problem in <svg style="vertical-align:-2.3205pt;width:75.262497px;" id="M1" height="15.0875" version="1.1" viewBox="0 0 75.262497 15.0875" width="75.262497" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,12.138)"><path id="x5B" d="M290 -163h-170v866h170v-28q-79 -7 -94 -19.5t-15 -72.5v-627q0 -59 14.5 -71.5t94.5 -19.5v-28z" /></g><g transform="matrix(.017,-0,0,-.017,5.927,12.138)"><path id="x30" d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105&#xA;q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" /></g><g transform="matrix(.017,-0,0,-.017,14.086,12.138)"><path id="x2C" d="M95 130q31 0 61 -30t30 -78q0 -53 -38 -87.5t-93 -51.5l-11 29q77 31 77 85q0 26 -17.5 43t-44.5 24q-4 0 -8.5 6.5t-4.5 17.5q0 18 15 30t34 12z" /></g><g transform="matrix(.017,-0,0,-.017,20.784,12.138)"><path id="x221E" d="M983 225q0 -112 -67 -174.5t-150 -62.5q-91 0 -154.5 43.5t-113.5 129.5q-49 -85 -104 -129t-138 -44q-98 0 -158.5 66t-60.5 154q0 59 21 106.5t54.5 75.5t70.5 43t73 15q90 0 152.5 -43.5t112.5 -128.5q48 84 104.5 128t140.5 44q93 0 155 -65t62 -158zM478 196&#xA;q-27 49 -47 80t-50 67t-64 54t-73 18q-48 0 -81.5 -47t-33.5 -128q0 -96 37.5 -157.5t99.5 -61.5q68 0 117.5 47t94.5 128zM889 204q0 91 -35.5 151t-99.5 60q-68 0 -119 -47t-95 -127q27 -49 47 -80.5t50 -67.5t65 -54t74 -18q113 0 113 183z" /></g><g transform="matrix(.017,-0,0,-.017,38.123,12.138)"><path id="x29" d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" /></g><g transform="matrix(.017,-0,0,-.017,47.778,12.138)"><path id="xD7" d="M528 54l-36 -38l-198 201l-198 -201l-36 38l197 200l-197 201l36 38l198 -202l198 202l36 -38l-197 -201z" /></g><g transform="matrix(.017,-0,0,-.017,61.547,12.138)"><path id="x1D437" d="M780 372q0 -191 -178 -297q-128 -75 -335 -75h-250l7 27q61 7 77 22t28 76l77 398q11 62 0 76.5t-77 22.5l6 28h292q164 0 258.5 -67.5t94.5 -210.5zM678 375q0 119 -73 180.5t-201 61.5q-62 0 -82 -13q-17 -7 -25 -53l-80 -427q-8 -47 -4 -62t26 -20q24 -6 80 -6&#xA;q166 0 262.5 95t96.5 244z" /></g></svg> for a class of linear parabolic partial differential equations. We assume that <svg style="vertical-align:-0.1092pt;width:53.025002px;" id="M2" height="16.887501" version="1.1" viewBox="0 0 53.025002 16.887501" width="53.025002" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,16.7)"><use xlink:href="#x1D437" /></g><g transform="matrix(.017,-0,0,-.017,18.421,16.7)"><path id="x2282" d="M512 1h-130q-127 0 -217 74.5t-90 179.5t90 179.5t217 74.5h130v-50h-131q-103 0 -175.5 -59.5t-72.5 -144.5t72.5 -144.5t175.5 -59.5h131v-50z" /></g><g transform="matrix(.017,-0,0,-.017,33.125,16.7)"><path id="x211D" d="M751 18q-1 -4 -2 -13t-2 -13q-24 0 -35 1q-57 3 -92.5 23t-69.5 68q-21 30 -101 160q-13 22 -30.5 31t-54.5 9h-32v-159q0 -62 14 -77t74 -20v-28h-382v28q62 5 76 19.5t14 77.5v400q0 63 -14 77.5t-76 19.5v28h372q109 0 159 -34q67 -42 67 -131q0 -115 -127 -172&#xA;q27 -52 89 -144q49 -71 81 -104q31 -36 72 -47zM543 469q0 76 -42 112t-104 36q-41 0 -54 -10q-11 -7 -11 -44v-247h48q73 0 108 29q55 42 55 124zM290 131v390q0 62 -7.5 79.5t-30.5 17.5q-24 0 -31.5 -17.5t-7.5 -79.5v-390q0 -62 7.5 -79.5t31.5 -17.5q23 0 30.5 17.5&#xA;t7.5 79.5z" /></g><g transform="matrix(.012,-0,0,-.012,45.725,8.538)"><path id="x1D451" d="M530 686q-79 -330 -126 -595q-5 -24 4 -24q22 0 77 53l16 -24q-42 -49 -88 -78.5t-72 -29.5q-37 0 -19 83l21 99h-2q-62 -83 -153 -141q-65 -41 -97 -41q-28 0 -48 31.5t-20 91.5q0 71 32.5 144t88.5 118q36 30 94 52.5t94 22.5q38 0 68 -13l29 158q7 40 2 47.5t-38 7.5&#xA;h-35l1 26q39 4 76 13.5t58.5 17t27.5 7.5q16 0 9 -26zM387 375q-11 11 -38.5 20t-51.5 9q-45 0 -79 -23q-46 -32 -77.5 -107.5t-31.5 -143.5q0 -40 9.5 -58.5t23.5 -18.5q40 0 113.5 70t99.5 118z" /></g></svg> is an
unbounded, open, connected set with regular boundary. Our hypotheses are unbounded and locally Lipschitz coefficients, not necessarily differentiable, with continuous data and local uniform ellipticity. We construct a classical solution to the nonhomogeneous Cauchy-Dirichlet problem using stochastic differential equations and parabolic differential equations in bounded domains.

Gerardo Rubio

The Cauchy-Dirichlet Problem for a Class of Linear Parabolic Differential Equations with Unbounded Coefficients in an Unbounded Domain

We study the valuation of the variance swaps under stochastic volatility with delay
and jumps. In our model, the volatility of the underlying stock price process not only
incorporates jumps, which are found to be active empirically, but also exhibits past dependence: the behavior of a stock price right after a given time <svg     style="vertical-align:-0.1638pt;width:5.9250002px;" id="M1" height="10.3875" version="1.1" viewBox="0 0 5.9250002 10.3875" width="5.9250002"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,10.125)"><path id="x1D461" d="M324 430l-26 -36l-112 -4l-55 -265q-13 -66 7 -66q13 0 44.5 20t50.5 40l17 -24q-38 -40 -85.5 -73.5t-87.5 -33.5q-50 0 -21 138l55 262h-80l-2 8l25 34h66l25 99l78 63l10 -9l-37 -153h128z" /></g>

		
	
</svg> depends not only on
the situation at <svg     style="vertical-align:-0.1638pt;width:5.9250002px;" id="M2" height="10.3875" version="1.1" viewBox="0 0 5.9250002 10.3875" width="5.9250002"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,10.125)"><use xlink:href="#x1D461"/></g>

		
	
</svg> but also on the whole past (history) of the process <svg     style="vertical-align:-2.3205pt;width:25.8375px;" id="M3" height="15.0875" version="1.1" viewBox="0 0 25.8375 15.0875" width="25.8375"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,12.138)"><path id="x1D446" d="M457 488l-30 -3q-17 148 -131 148q-53 0 -84.5 -34.5t-31.5 -82.5q0 -42 25.5 -72t74.5 -62l33 -22q63 -42 95 -85t32 -102q0 -84 -67 -137t-163 -53q-58 0 -113 22t-70 43l-4 152l27 4q4 -32 15 -62.5t31 -59.5t53.5 -47t76.5 -18q56 0 92 35t36 96q0 39 -25 70t-78 68&#xA;l-31 22q-32 23 -53.5 41.5t-45 57t-23.5 77.5q0 82 58 132.5t156 50.5q46 0 101 -17l18.5 -6t17 -6t8.5 -3q-4 -55 0 -147z" /></g><g transform="matrix(.017,-0,0,-.017,8.222,12.138)"><path id="x28" d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" /></g><g transform="matrix(.017,-0,0,-.017,14.103,12.138)"><use xlink:href="#x1D461"/></g><g transform="matrix(.017,-0,0,-.017,19.9,12.138)"><path id="x29" d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" /></g>

		
	
</svg> up to time <svg     style="vertical-align:-0.1638pt;width:5.9250002px;" id="M4" height="10.3875" version="1.1" viewBox="0 0 5.9250002 10.3875" width="5.9250002"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,10.125)"><use xlink:href="#x1D461"/></g>

		
	
</svg> as well. 
The jump part in our model is finally represented by a general version of compound
Poisson processes. We provide some analytical closed forms for the expectation of the
realized variance for the stochastic volatility with delay and jumps. We also present a
lower bound for delay as a measure of risk. As applications of our analytical solutions,
a numerical example using <i  >S&#x26;P</i>60 Canada Index (1998&#x2013;2002) is then provided to price
variance swaps.

Anatoliy Swishchuk

Li Xu

Pricing Variance Swaps for Stochastic Volatilities with Delay and Jumps

We provide a stochastic analysis of hard disk performance, including a closed
form solution for the average access time of a memory request. The model we use
covers a wide range of types and applications of disks, and in particular it captures
modern innovations like zone bit recording. The derivation is based on an analytical
technique we call &#x201c;shuffling&#x201d;, which greatly simplifies the analysis relative to
previous work and provides a simple, easy-to-use formula for the average access
time. 
Our analysis can predict performance of single disks for a wide range of disk
types and workloads. Furthermore, it can predict the performance benefits of several
optimizations, including short stroking and mirroring, which are common in
disk arrays.

Field Cady

Yi Zhuang

Mor Harchol-Balter

A Stochastic Analysis of Hard Disk Drives

Let <svg style="vertical-align:-2.3205pt;width:31.15px;" id="M1" height="15.0875" version="1.1" viewBox="0 0 31.15 15.0875" width="31.15" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,12.138)"><path id="x1D44B" d="M775 650l-6 -28q-60 -6 -81.5 -16t-61.5 -54l-175 -191l125 -243q30 -58 48.5 -71t82.5 -19l-5 -28h-275l7 28l35 4q31 4 37 12t-6 34l-108 216q-140 -165 -177 -219q-16 -22 -10.5 -30.5t41.5 -13.5l22 -3l-7 -28h-244l8 28q52 4 75 15.5t67 52.5q48 46 206 231&#xA;l-110 215q-26 51 -44 63t-72 17l6 28h250l-6 -28l-27 -4q-30 -5 -35 -10t3 -27q17 -43 95 -190q70 78 154 185q15 21 10 29.5t-33 12.5l-30 4l5 28h236z" /></g><g transform="matrix(.017,-0,0,-.017,13.526,12.138)"><path id="x28" d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" /></g><g transform="matrix(.017,-0,0,-.017,19.407,12.138)"><path id="x1D461" d="M324 430l-26 -36l-112 -4l-55 -265q-13 -66 7 -66q13 0 44.5 20t50.5 40l17 -24q-38 -40 -85.5 -73.5t-87.5 -33.5q-50 0 -21 138l55 262h-80l-2 8l25 34h66l25 99l78 63l10 -9l-37 -153h128z" /></g><g transform="matrix(.017,-0,0,-.017,25.204,12.138)"><path id="x29" d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" /></g></svg> be a controlled one-dimensional standard Brownian motion starting from <svg style="vertical-align:-2.3205pt;width:75.362503px;" id="M2" height="15.1125" version="1.1" viewBox="0 0 75.362503 15.1125" width="75.362503" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path id="x1D465" d="M536 404q0 -17 -13.5 -31.5t-26.5 -14.5q-8 0 -15 10q-11 14 -25 14q-22 0 -67 -50q-47 -52 -68 -82l37 -102q31 -88 55 -88t78 59l16 -23q-32 -48 -68.5 -78t-65.5 -30q-19 0 -37.5 20t-29.5 53l-41 116q-72 -106 -114.5 -147.5t-79.5 -41.5q-21 0 -34.5 14t-13.5 37&#xA;q0 16 13.5 31.5t28.5 15.5q12 0 17 -11q5 -10 25 -10q22 0 57.5 36t89.5 111l-40 108q-22 58 -36 58q-21 0 -67 -57l-19 20q81 107 125 107q17 0 30 -22t39 -88l22 -55q68 92 108.5 128.5t74.5 36.5q20 0 32.5 -14t12.5 -30z" /></g><g transform="matrix(.017,-0,0,-.017,14.273,12.162)"><path id="x2208" d="M448 1h-83q-118 0 -201.5 74.5t-83.5 179.5t83.5 179.5t201.5 74.5h83v-50h-84q-87 0 -150.5 -51.5t-73.5 -127.5h308v-50h-308q10 -76 73.5 -127.5t150.5 -51.5h84v-50z" /></g><g transform="matrix(.017,-0,0,-.017,27.974,12.162)"><use xlink:href="#x28" /></g><g transform="matrix(.017,-0,0,-.017,33.856,12.162)"><path id="x2212" d="M535 230h-483v50h483v-50z" /></g><g transform="matrix(.017,-0,0,-.017,43.834,12.162)"><path id="x1D451" d="M530 686q-79 -330 -126 -595q-5 -24 4 -24q22 0 77 53l16 -24q-42 -49 -88 -78.5t-72 -29.5q-37 0 -19 83l21 99h-2q-62 -83 -153 -141q-65 -41 -97 -41q-28 0 -48 31.5t-20 91.5q0 71 32.5 144t88.5 118q36 30 94 52.5t94 22.5q38 0 68 -13l29 158q7 40 2 47.5t-38 7.5&#xA;h-35l1 26q39 4 76 13.5t58.5 17t27.5 7.5q16 0 9 -26zM387 375q-11 11 -38.5 20t-51.5 9q-45 0 -79 -23q-46 -32 -77.5 -107.5t-31.5 -143.5q0 -40 9.5 -58.5t23.5 -18.5q40 0 113.5 70t99.5 118z" /></g><g transform="matrix(.017,-0,0,-.017,53.269,12.162)"><path id="x2C" d="M95 130q31 0 61 -30t30 -78q0 -53 -38 -87.5t-93 -51.5l-11 29q77 31 77 85q0 26 -17.5 43t-44.5 24q-4 0 -8.5 6.5t-4.5 17.5q0 18 15 30t34 12z" /></g><g transform="matrix(.017,-0,0,-.017,59.983,12.162)"><use xlink:href="#x1D451" /></g><g transform="matrix(.017,-0,0,-.017,69.417,12.162)"><use xlink:href="#x29" /></g></svg>. The problem of optimally controlling <svg style="vertical-align:-2.3205pt;width:31.15px;" id="M3" height="15.0875" version="1.1" viewBox="0 0 31.15 15.0875" width="31.15" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,12.138)"><use xlink:href="#x1D44B" /></g><g transform="matrix(.017,-0,0,-.017,13.526,12.138)"><use xlink:href="#x28" /></g><g transform="matrix(.017,-0,0,-.017,19.407,12.138)"><use xlink:href="#x1D461" /></g><g transform="matrix(.017,-0,0,-.017,25.204,12.138)"><use xlink:href="#x29" /></g></svg> until <svg style="vertical-align:-2.3205pt;width:68.949997px;" id="M4" height="15.1125" version="1.1" viewBox="0 0 68.949997 15.1125" width="68.949997" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path id="x7C" d="M162 -163h-61v866h61v-866z" /></g><g transform="matrix(.017,-0,0,-.017,4.533,12.162)"><use xlink:href="#x1D44B" /></g><g transform="matrix(.017,-0,0,-.017,17.996,12.162)"><use xlink:href="#x28" /></g><g transform="matrix(.017,-0,0,-.017,23.878,12.162)"><use xlink:href="#x1D461" /></g><g transform="matrix(.017,-0,0,-.017,29.674,12.162)"><use xlink:href="#x29" /></g><g transform="matrix(.017,-0,0,-.017,35.556,12.162)"><use xlink:href="#x7C" /></g><g transform="matrix(.017,-0,0,-.017,44.735,12.162)"><path id="x3D" d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" /></g><g transform="matrix(.017,-0,0,-.017,59.439,12.162)"><use xlink:href="#x1D451" /></g></svg> for the first time is solved explicitly in a particular case. The maximal value that the instantaneous reward given for survival in <svg style="vertical-align:-2.3205pt;width:47.4375px;" id="M5" height="15.1125" version="1.1" viewBox="0 0 47.4375 15.1125" width="47.4375" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,12.162)"><use xlink:href="#x28" /></g><g transform="matrix(.017,-0,0,-.017,5.944,12.162)"><use xlink:href="#x2212" /></g><g transform="matrix(.017,-0,0,-.017,15.922,12.162)"><use xlink:href="#x1D451" /></g><g transform="matrix(.017,-0,0,-.017,25.357,12.162)"><use xlink:href="#x2C" /></g><g transform="matrix(.017,-0,0,-.017,32.054,12.162)"><use xlink:href="#x1D451" /></g><g transform="matrix(.017,-0,0,-.017,41.488,12.162)"><use xlink:href="#x29" /></g></svg> can take is determined.

Mario Lefebvre

Maximizing the Mean Exit Time of a Brownian Motion from an Interval

The object of this paper is to study the stability behaviours of the deterministic
and stochastic versions of a two-species symmetric competition model. The logistic
parameters of the competitive species are perturbed by colored noises or Ornstein-Uhlenbeck
processes due to random environment. The Fokker-Planck equation has been used to obtain
probability density functions. Here, we have also discussed the relationship between stability
behaviours of this model in a deterministic environment and the corresponding model in a
stochastic environment.

G. P. Samanta

A Stochastic Two Species Competition Model: Nonequilibrium Fluctuation and Stability

We use the <svg style="vertical-align:-3.50804pt;width:8.4750004px;" id="M2" height="12.1125" version="1.1" viewBox="0 0 8.4750004 12.1125" width="8.4750004" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D45E" /></g></svg>-Weibull distribution and define a new counting process using the fractional order. As a consequence, we introduce a <svg style="vertical-align:-3.50804pt;width:8.4750004px;" id="M3" height="12.1125" version="1.1" viewBox="0 0 8.4750004 12.1125" width="8.4750004" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D45E" /></g></svg>-process with <svg style="vertical-align:-3.50804pt;width:8.4750004px;" id="M4" height="12.1125" version="1.1" viewBox="0 0 8.4750004 12.1125" width="8.4750004" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D45E" /></g></svg>-Weibull interarrival times. Some interesting special cases are also discussed which leads to a Mittag-Leffler form.

Kunnummal Muralidharan

Seema S. Nair

A<svg style="vertical-align:-3.50804pt" height="12.1125" version="1.1" viewBox="0 0 8.4750004 12.1125" width="8.4750004" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
		<g transform="matrix(.017,-0,0,-.017,.062,7.675)">
			<path id="x1D45E" d="M474 429q-19 -69 -47 -222l-65 -347q-8 -49 0 -60t49 -16l26 -3l-4 -26l-246 -12l4 25l17 3q37 6 50 20.5t23 60.5l67 321h-2q-65 -79 -150 -138q-69 -47 -104 -47q-28 0 -48.5 32t-20.5 81q0 78 35 148t90 117q67 57 161 77q23 5 58 5q43 0 90 -15zM387 387 q-30 16 -75 16q-58 0 -92 -27q-49 -39 -78.5 -112t-29.5 -136q0 -34 8.5 -52.5t21.5 -18.5q40 0 109.5 63.5t103.5 115.5q16 53 32 151z"/>
		</g>
	</svg>-Weibull Counting Process through a Fractional Differential Operator

Using an integral equation associated with generalized backward Kolmogorov's equation for
the transition probability density function, recurrence relations are derived for the moments
of the time of first exit of jump-diffusions with Markovian switching. The results are used
to find the expectation of first passage time of some financial models.

Jun Peng

Zaiming Liu

First Passage Time Moments of Jump-Diffusions with Markovian Switching

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International Journal of Stochastic Analysis - Table of contents 2011

International Journal of Stochastic Analysis | Hindawi

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International Journal of Stochastic Analysis

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International Journal of Stochastic Analysis