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Keywords
(4)
Stochastic Integral
Strong Approximation
Uniform Convergence
Random Walk
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Stochastic Integration Based on Simple, Symmetric Random Walks
Stochastic Integration Based on Simple, Symmetric Random Walks,10.1007/s1095900701408,Journal of Theoretical Probability,Tamás Szabados,Balázs Szék
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Stochastic Integration Based on Simple, Symmetric Random Walks
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Tamás Szabados
,
Balázs Székely
A new approach to stochastic integration is described, which is based on an a.s. pathwise approximation of the integrator by simple, symmetric random walks. Hopefully, this method is didactically more advantageous, more transparent, and technically less demanding than other existing ones. In a large part of the theory one has a.s.
uniform convergence
on compacts. In particular, the method gives a.s. convergence for the
stochastic integral
of a finite variation function of the integrator, which is not càdlàg in general.
Journal:
Journal of Theoretical Probability  J THEOR PROBABILITY
, vol. 22, no. 1, pp. 203219, 2009
DOI:
10.1007/s1095900701408
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Citation Context
(1)
...Now let me recall some important facts from [17, 18] and [
19
] about the “twist and shrink” construction that will be used in the sequel...
Tamás Szabados
.
Selfintersection Local Time of Planar Brownian Motion Based on a Stro...
References
(13)
On pathwise stochastic integration
(
Citations: 22
)
Rajeeva L. Karandikar
Journal:
Stochastic Processes and Their Applications  STOCH PROC APPL
, vol. 57, no. 1, pp. 1118, 1995
On the Random Walk and Brownian Motion
(
Citations: 21
)
Frank B. Knight
Journal:
Transactions of The American Mathematical Society  TRANS AMER MATH SOC
, vol. 103, no. 2, pp. 218218, 1962
Continuous martingales and brownian motion
(
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)
D. Revuz
,
M. Yor
Published in 1991.
A discrete It^o''s formula
(
Citations: 5
)
T. Szabados
Published in 1989.
An elementary introduction to the Wiener process and stochastic integrals
(
Citations: 10
)
Tamas Szabados
Published in 2010.
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Citations
(1)
Selfintersection Local Time of Planar Brownian Motion Based on a Strong Approximation by Random Walks
Tamás Szabados
Journal:
Journal of Theoretical Probability  J THEOR PROBABILITY
, pp. 138, 2010