000 03886nam a22005175i 4500
001 978-0-387-25175-2
003 DE-He213
005 20170628033240.0
007 cr nn 008mamaa
008 100301s2005 xxu| s |||| 0|eng d
020 _a9780387251752
_9978-0-387-25175-2
024 7 _a10.1007/b106901
_2doi
050 4 _aTA329-348
050 4 _aTA640-643
072 7 _aTBJ
_2bicssc
072 7 _aMAT003000
_2bisacsh
082 0 4 _a519
_223
100 1 _aSitu, Rong.
_eauthor.
245 1 0 _aTheory of Stochastic Differential Equations with Jumps and Applications
_h[electronic resource] :
_bMathematical and Analytical Techniques with Applications to Engineering /
_cby Rong Situ.
264 1 _aBoston, MA :
_bSpringer US,
_c2005.
300 _aXX, 434 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aStochastic Differential Equations with Jumps in Rd -- Martingale Theory and the Stochastic Integral for Point Processes -- Brownian Motion, Stochastic Integral and Ito's Formula -- Stochastic Differential Equations -- Some Useful Tools in Stochastic Differential Equations -- Stochastic Differential Equations with Non-Lipschitzian Coefficients -- Applications -- How to Use the Stochastic Calculus to Solve SDE -- Linear and Non-linear Filtering -- Option Pricing in a Financial Market and BSDE -- Optimal Consumption by H-J-B Equation and Lagrange Method -- Comparison Theorem and Stochastic Pathwise Control -- Stochastic Population Control and Reflecting SDE -- Maximum Principle for Stochastic Systems with Jumps.
520 _aThis book is written for people who are interested in stochastic differential equations (SDEs) and their applications. It shows how to introduce and define the Ito integrals, to establish Ito’s differential rule (the so-called Ito formula), to solve the SDEs, and to establish Girsanov’s theorem and obtain weak solutions of SDEs. It also shows how to solve the filtering problem, to establish the martingale representation theorem, to solve the option pricing problem in a financial market, and to obtain the famous Black-Scholes formula, along with other results. In particular, the book will provide the reader with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, and science. Theory of Stochastic Differential Equations with Jumps and Applications will be a valuable reference for grad students and professionals in physics, chemistry, biology, engineering, finance and mathematics who are interested in problems such as the following: mathematical description and analysis of stocks and shares; option pricing, optimal consumption, arbitrage-free markets; control theory and stochastic control theory and their applications; non-linear filtering problems with jumps; population control.
650 0 _aEngineering.
650 0 _aMathematics.
650 0 _aMathematical physics.
650 0 _aEngineering mathematics.
650 0 _aHydraulic engineering.
650 0 _aFinance.
650 1 4 _aEngineering.
650 2 4 _aAppl.Mathematics/Computational Methods of Engineering.
650 2 4 _aApplications of Mathematics.
650 2 4 _aMathematical and Computational Physics.
650 2 4 _aEngineering Fluid Dynamics.
650 2 4 _aFinancial Economics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387250830
856 4 0 _uhttp://dx.doi.org/10.1007/b106901
912 _aZDB-2-ENG
999 _c14317
_d14317