Stochastic invariance in infinite dimension beyond Lipschitz coefficients
84 ...
Jaber, Eduardo Abi, Tappe, Stefan
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On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients
The Annals of Probability, 2006 39 ...
Mytnik, Leonid +2 more
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On a high-dimensional nonlinear stochastic partial differential equation
, 2014 International audienceIn this paper we investigate a nonlinear stochastic partial differential equation perturbed by a space-correlated Gaussian noise in arbitrary dimensiond>1, with a non-Lipschitz coefficient noisy term. The equation studied coincides
Mellouk, Mohamed, Boulanba, Lahcen
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Fourier Mass Lower Bounds for Batchelor‐Regime Passive Scalars
Communications on Pure and Applied Mathematics, Volume 79, Issue 6, Page 1449-1466, June 2026.ABSTRACT Batchelor predicted that a passive scalar ψν$\psi ^\nu$ with diffusivity ν$\nu$, advected by a smooth fluid velocity, should typically have Fourier mass distributed as |ψ̂ν|2(k)≈|k|−d$|\widehat{\psi }^\nu |^2(k) \approx |k|^{-d}$ for |k|≪ν−1/2$|k| \ll \nu ^{-1/2}$.
William Cooperman, Keefer Rowan
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PATHWISE UNIQUENESS OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY CAUCHY PROCESSES WITH DRIFT [PDF]
We consider one-dimensional stochastic differential equations driven by Cauchy processes with drift. This driving process is also known as a strictly 1-stable process.
Tsukada, Hiroshi
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Strong convergence of Euler-type methods for nonlinear stochastic differential equations [PDF]
, 2002 Traditional finite-time convergence theory for numerical methods applied to stochastic differential equations (SDEs) requires a global Lipschitz assumption on the drift and diffusion coefficients.
Stuart, Andrew M. +6 more
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On MAP Estimates and Source Conditions for Drift Identification in SDEs
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 2, June 2026.ABSTRACT We consider the inverse problem of identifying the drift in an stochastic differential equation (SDE) from n$n$ observations of its solution at M+1$M+1$ distinct time points. We derive a corresponding maximum a posteriori (MAP) estimate, we prove differentiability properties as well as a so‐called tangential cone condition for the forward ...
Daniel Tenbrinck +3 more
wiley +1 more source
Efficient Deconvolution in Populational Inverse Problems
International Journal for Numerical Methods in Engineering, Volume 127, Issue 9, 15 May 2026.ABSTRACT This work is focused on the inversion task of inferring the distribution over parameters of interest, leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by the increasing availability of data, but a major roadblock is blind deconvolution, arising when the observational noise ...
Arnaud Vadeboncoeur +2 more
wiley +1 more source
A note on the rate of convergence of the Euler-Maruyama method for stochastic differential equations
, 2008 The recent article [2] reveals the strong convergence of the Euler-Maruyama solution to the exact solution of a stochastic differential equation under the local Lipschitz condition. However, it does not provide us with an order of convergence.
Yuan, C., Mao, X., Chenggui Yuan
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Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients
Stochastic Processes and their Applications, 1995 The author considers the following backward stochastic differential equation \[ x(t) = \int^1_tf \bigl( s,x(s), y(s) \bigr) ds + \int^1_t \biggl[ g \bigl( s,x (s) \bigr) + y( s) \biggr] dw(s) = X \tag{*} \] on \(0 \leq t \leq 1\). Here \(w(t)\) in a \(q\)-dimensional Brownian motion and \(y(t)\) is an adapted control process.
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