Question

Why can the solution of a SPDE $\partial_tu(t,x)=\cdots$ be viewed as a stochastic process indexed by $t$ with values in a space of functions of $x$?

score 132 · Answer 1 · 2026-04-03 05:52:36

132

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Why can the solution of a SPDE $\partial_tu(t,x)=\cdots$ be viewed as a stochastic process indexed by $t$ with values in a space of functions of $x$?

Published on 03 Apr 2026 - 5:52

score 204 · Answer 2 · 2026-02-23 10:22:03

204

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Recast the scalar SPDE $du_t(Φ_t(x))=f_t(Φ_t(x))dt+∇ u_t(Φ_t(x))⋅ξ_t(Φ_t(x))dW_t$ into a SDE in an infinite dimensional function space.

Published on 23 Feb 2026 - 10:22

score 3.1k · Answer 3 · 2026-02-23 10:18:26

3.1k

Views

Intuitive explanation of a stochastic PDE

Published on 23 Feb 2026 - 10:18

score 238 · Answer 4 · 2026-02-23 10:14:11

238

Views

Checking a proof using Markov's Inequality

Published on 23 Feb 2026 - 10:14

score 125 · Answer 5 · 2026-02-23 10:16:19

125

Views

Stochastic Representation of Boundary Value Problem

Published on 23 Feb 2026 - 10:16

score 21 · Answer 6 · 2026-02-23 10:16:20

21

Views

How can I construct a stochastic model from a deterministic one (dealing with population dynamics)

Published on 23 Feb 2026 - 10:16

score 73 · Answer 7 · 2026-02-23 10:18:25

73

Views

What is a good recentish book on numerical algorithms for stiff non-linear PDEs?

Published on 23 Feb 2026 - 10:18

score 972 · Answer 8 · 2026-02-23 10:23:38

972

Views

Heston model (which is a Stochastic volatility model) Ito's lemma

Published on 23 Feb 2026 - 10:23

score 7.9k · Answer 9 · 2026-02-23 10:14:12

7.9k

Views

Ito formula for jump-Diffusion

Published on 23 Feb 2026 - 10:14

score 86 · Answer 10 · 2026-02-23 10:16:19

86

Views

Corresponding Stochastic Differential Equation to a reaction Diffusion Equation

Published on 23 Feb 2026 - 10:16

score 260 · Answer 11 · 2026-02-23 10:20:08

260

Views

Construction of the quadratic variation for Hilbert space valued local martingales

Published on 23 Feb 2026 - 10:20

score 76 · Answer 12 · 2026-02-23 10:20:48

76

Views

On the defninition of white noise, a question concerning the notes on SPDE's from Walsh

Published on 23 Feb 2026 - 10:20

score 89 · Answer 13 · 2026-02-23 10:20:31

89

Views

Recovering White noise from the Brownian Sheet. A question concerning the notes on SPDE's from Walsh.

Published on 23 Feb 2026 - 10:20

score 115 · Answer 14 · 2026-02-23 10:21:49

115

Views

Computing the covariance of a solution to the stochastic heat equation. A question concerning the notes on SPDE' s of Hairer

Published on 23 Feb 2026 - 10:21

score 73 · Answer 15 · 2026-02-23 10:15:00

73

Views

Itô's Lemma and expected values

Published on 23 Feb 2026 - 10:15

List Question

Why can the solution of a SPDE $\partial_tu(t,x)=\cdots$ be viewed as a stochastic process indexed by $t$ with values in a space of functions of $x$?

Recast the scalar SPDE $du_t(Φ_t(x))=f_t(Φ_t(x))dt+∇ u_t(Φ_t(x))⋅ξ_t(Φ_t(x))dW_t$ into a SDE in an infinite dimensional function space.

Intuitive explanation of a stochastic PDE

Checking a proof using Markov's Inequality

Stochastic Representation of Boundary Value Problem

How can I construct a stochastic model from a deterministic one (dealing with population dynamics)

What is a good recentish book on numerical algorithms for stiff non-linear PDEs?

Heston model (which is a Stochastic volatility model) Ito's lemma

Ito formula for jump-Diffusion

Corresponding Stochastic Differential Equation to a reaction Diffusion Equation

Construction of the quadratic variation for Hilbert space valued local martingales

On the defninition of white noise, a question concerning the notes on SPDE's from Walsh

Recovering White noise from the Brownian Sheet. A question concerning the notes on SPDE's from Walsh.

Computing the covariance of a solution to the stochastic heat equation. A question concerning the notes on SPDE' s of Hairer

Itô's Lemma and expected values

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