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Martingale and independence

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#probability-theory #stochastic-processes #stochastic-calculus #martingales
65
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solve the SDE $dX_t=-\frac{1}{2}\exp\{-2X_t\}dt+\exp\{-X_t\}dW_t$

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#stochastic-calculus #stochastic-differential-equations
362
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Lebesgue-Stieltjes Integration by parts formula

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#integration #measure-theory #stochastic-calculus #stieltjes-integral
77
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Rewriting a stochastic integral

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#stochastic-processes #stochastic-calculus #stochastic-integrals
64
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Binomial distribution approximated by normal distribution: How to arrive at this identity?

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#stochastic-processes #normal-distribution #stochastic-calculus #binomial-distribution
71
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$(a)$ Calculate $P(X_5>0|W_3=1)$ given that $\{W_t\}$ is an Simple Brownian Motion and $\{X_t\}$ a stochastic process

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#stochastic-processes #stochastic-calculus #conditional-probability #brownian-motion
119
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Show markov property for a s.p. with independent increment

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#stochastic-processes #stochastic-calculus
44
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Can I use the Chebychev inequality to prove this statement?

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#probability #probability-theory #expected-value #stochastic-calculus
94
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How can I prove that $\Bbb{P}(X>0)\geq \frac{\Bbb{E}(X)^2}{\Bbb{E}(X^2)}$

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#probability #probability-theory #expected-value #stochastic-calculus #cauchy-schwarz-inequality
95
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Prove that realized variance converges in probability to integrated variance for Ito process

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#stochastic-processes #stochastic-calculus #finance #stochastic-differential-equations
228
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How to calculate the autocorrelation of Ornstein Uhlenbeck process

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#stochastic-processes #stochastic-calculus
37
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Question on Markov property

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#stochastic-calculus #stochastic-integrals #stochastic-analysis #stochastic-differential-equations
113
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Decompose the Laplace transform of autocorrelation function of a stachastic process using Wiener-Kolmogorov whitening procedure

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#reference-request #stochastic-processes #stochastic-calculus #stochastic-differential-equations
60
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Markov alternative definition

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#stochastic-processes #stochastic-calculus #stochastic-integrals #stochastic-analysis
382
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Does there exist a version of the Burkholder-Davis-Gundy inequality for multidimensional continuous local martingales?

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

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