Born in 1972 in the family of musicians Alexander began his studies under the guidance of his father. After successful appearances at the regional competitions he was accepted to the Special Music School at the Novosibirsk State conservatory where he worked with Prof. M.Liberman..
In 1990 Alexander was honored as the one of Prize-winners at the very first International competition in his life - Premio Paganini in Genova. In 1991-97 Trostiansky had a luck to work with Prof. Irina Bochkova at the Moscow Tchaikovsky conservatory. 
Regular concerts brought artistic experience to the young musician, helped him to win another prestigious international competitions including
1996 - "Centre d'Arts" (Orford, Canada, 1st prize)
1997 - "F.Schubert and 20th Century Music" (Graz, Austria, 3rd prize)
1998 - "P.I. Tchaikovsky" (Moscow, 5th prize)

He participated in "Moscow Autumn", "Musik im Michel", "December Evenings by S.Richter", "Oleg Kagan Musikfest" (Kreuth), Y.Bashmet's festivals (Yaroslavl and Minsk) and many others.
Alexander is a regular recording artist. He recorded with "Melodia", "Vista Vera", "Chandos", "Dowani", "Egan Records", "Naxos", "ECM Records" labels, for Radio-1-Russia and "Orpheus-Radio".
Geography of his performances is extremely wide: more then 80 cities of Russia, over 30 countries of the world.

Trostiansky appeared in Grand Halls of the Moscow Conservatory and St.Petersburg Philharmonic, Concert-en Congresgebouw de Doelen, Jurriaanse Zaal (Rotterdam, Holland), Linbury Studio Theatre, Covent Garden (London), Mozarteum (Salzburg), Goetheanum (Dornach, Switzerland), Kravis Performing Arts Center (West Palm Beach), Schoenberg Hall (Los Angeles), Herbst Theatre (San-Francisco), Weill Hall at Carnegie Hall (New York).

His wide repertoire includes over sixty violin concertos, a lot of chamber music and music of 20th century. Some of modern Russian composers dedicated to him their works.
Amongst many other programs Trostiansky rendered Paganini's "24 capriccios" at once.

In 2001-2002 Alexander works as an expert at "The Window to Russia" philharmonics competition.
In 2007 Trostiansky has been given "The Honoured Artist of Russia" title.

His stage partners were such musicians as A.Lubimov, A.Rudin, N.Gutman, E.Virsaladze, V.Kholodenko, A.Melnikov, A.Bouzlov, D.Shapovalov.
Recently he made National Premieres of W.Schumann's and K.Weill's Violin Concertos, O.Messian's Fantasia for violin and piano, recorded monographic CDs with Russian composers' E.Sherbakov, V.Tarakanov and A.Muravlev music (all with "Classical Records" label).