List questions from stochastic-processes

Published on 26 Mar 2026 - 12:53

76

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A proof that $\sum_{i=0}^{p_n-1} f(Y_{t_i^n})(X_{t_{i+1}^n}-X_{t_i^n})^2$ converges a.s. to $\int_0^t f(Y_s)\mathrm{d}\langle X, X\rangle_s$

Published on 18 Apr 2026 - 2:19

225

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Time-dependent drift in an SDE

Published on 15 Apr 2026 - 4:48

47

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Numerical SDE Simulation for non-Gaussian?

Published on 13 Apr 2026 - 16:33

193

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understanding the proof that $dB_t^k dB_t^j = 0$ for $j\neq k$ for Brownian Motions

Published on 11 Apr 2026 - 9:56

77

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Brownian motion and geometric series convergence

Published on 12 Apr 2026 - 19:22

82

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Comparison of Solutions to SDEs

Published on 12 Apr 2026 - 13:43

112

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Stationary distribution of gradient-biased random walk

Published on 11 May 2026 - 5:28

138

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Transition derivative for Continuous Time Markov Chains notation

Published on 13 Apr 2026 - 18:11

38

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Mean sojourn time for reflected Brownian motion

Published on 14 Apr 2026 - 21:15

35

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The last visit chance of a biased random walk on a circle

Published on 11 Apr 2026 - 23:44

47

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Use Stirling's formula to prove probability of the event visits the origin after 2n steps

Published on 10 Apr 2026 - 17:23

348

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Let $(M_t)$ be a continuous square-integrable martingale with independent increments. Is $t \mapsto \mathbb E[M_t^2]$ continuous?

Published on 14 Apr 2026 - 12:27

79

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Solving a Stochastic Dynamic Programming with Vector State

Published on 10 May 2026 - 16:50

58

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Problem 2.7.1 in Karatzas and Shreve

Published on 10 May 2026 - 23:34

List Question

Natural filtration of the Brownian motion is not right-continuous

A proof that $\sum_{i=0}^{p_n-1} f(Y_{t_i^n})(X_{t_{i+1}^n}-X_{t_i^n})^2$ converges a.s. to $\int_0^t f(Y_s)\mathrm{d}\langle X, X\rangle_s$

Time-dependent drift in an SDE

Numerical SDE Simulation for non-Gaussian?

understanding the proof that $dB_t^k dB_t^j = 0$ for $j\neq k$ for Brownian Motions

Brownian motion and geometric series convergence

Comparison of Solutions to SDEs

Stationary distribution of gradient-biased random walk

Transition derivative for Continuous Time Markov Chains notation

Mean sojourn time for reflected Brownian motion

The last visit chance of a biased random walk on a circle

Use Stirling's formula to prove probability of the event visits the origin after 2n steps

Let $(M_t)$ be a continuous square-integrable martingale with independent increments. Is $t \mapsto \mathbb E[M_t^2]$ continuous?

Solving a Stochastic Dynamic Programming with Vector State

Problem 2.7.1 in Karatzas and Shreve

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