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adapted, increasing, (locally) integrable variation process is a (local) submartingale

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#probability-theory #stochastic-processes #stochastic-calculus #conditional-probability #stochastic-analysis
187
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Deterministic Integral of a Predictable Process is Predictable

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#stochastic-processes #stochastic-calculus #stochastic-integrals #stochastic-pde
159
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How can I use the moment generating function to prove independence between $X_s$ and $X_t-X_s$

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#probability #stochastic-processes #stochastic-calculus
63
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Standard Brownian motion almost surely not $0$.

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#probability-theory #stochastic-processes #stochastic-calculus #stochastic-analysis #stochastic-pde
703
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Local martingale up to a stopping time vs local martingale

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#probability-theory #stochastic-processes #stochastic-calculus
284
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Geometric Brownian Motion as the limit of Binomial Tree

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#stochastic-processes #stochastic-calculus #time-series
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Solve SDE for Brownian Bridge

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#stochastic-calculus #brownian-motion #stochastic-differential-equations
87
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Progressively Measurable on a Topological Space

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#measure-theory #stochastic-processes #stochastic-calculus #stochastic-analysis
62
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Fourier expansion of bounded noise

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#stochastic-processes #fourier-series #stochastic-calculus
3k
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Supremum of Brownian motion

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#stochastic-processes #stochastic-calculus #brownian-motion #stochastic-analysis
75
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Limit in distribution of increasing variance normal random variable

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#functional-analysis #stochastic-calculus
1k
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Conditional expectation for Brownian motion

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#probability-theory #stochastic-processes #stochastic-calculus #brownian-motion #stopping-times
111
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Doobs Martingale inequality

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#stochastic-processes #stochastic-calculus #brownian-motion
498
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Are $\int_0^t \text{sign}(W_u) \, dW_u$ and $W_t$ independent for a Brownian motion $(W_t)_{t \geq 0}$?

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#probability-theory #stochastic-processes #stochastic-calculus #brownian-motion
81
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Example of ANY stochastic process (SDE), with reversible distribution

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#stochastic-processes #stochastic-calculus #stochastic-analysis #stationary-processes

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